# Overlap distribution in the multiple spherical SK models (joint work Michel Talagrand).

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One possible approach to the study of the geometry of the Gibbs measure in the Sherrington-Kirkpatrick

type models (for example, the chaos and ultrametricity problems) is based on the analysis of the free energy

on several replicas of the system under some constraints on the distances between replicas. In general, this

approach runs into serious technical difficulties, but we were able to make some progress in the setting of the

spherical p-spin SK models where many computations become more explicit.